In the present paper we propose a new approach for modeling propagating failures which occur with a time delay with respoect to the initiating failure. The approach is b ased on the Kolmogorov-Dmitriev theory of branching stochastic processes for the description of the interaction between an initiating failure of a component and the consequent behaviour of the other components of the system. When a component fails, it can stochastically initiate failures on a number of other compoents according to given multivariate probabilistic laws. The propagation of the failures, however, is not instantaneous so that the successive failures of the components occur with a stochastic time delay, similarly to the way delayed neutrons are emitted by their precursors in a nuclear reactor.
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